# Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence

## TL;DR

This paper confirms through simulations that anisotropic MHD turbulence exhibits a steady ratio of parallel to perpendicular similarity lengths during decay, supporting a theoretical similarity solution and revealing a Taylor–Kármán-like decay behavior.

## Contribution

The study validates the similarity hypothesis in anisotropic MHD turbulence and demonstrates a steady ratio of length scales during decay using direct numerical simulations.

## Key findings

- The ratio of parallel to perpendicular length scales fluctuates around a steady value.
- A Taylor–Kármán-like similarity decay is observed in MHD turbulence.
- The parameters like Reynolds number and magnetic field influence the decay behavior.

## Abstract

In an earlier paper (Wan et al. 2012), the authors showed that a similarity solution for anisotropic incompressible 3D magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\vB_0$, exists if the ratio of parallel to perpendicular (with respect to $\vB_0$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor--K\'arm\'an-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, DC field strength, and cross-helicity, on the nature of similarity decay is discussed.